WiFi: I use my phone for music and navigation. The mini will pair with the phone for calling and navigation, but I have to use a wire to play internet radio.

I meant Mini Bluetooth, not WiFi.

Yes, you need to get a Bluetooth receiver like this one: BriteLink Bluetooth Receiver for iPhone Dock. https://www.amazon.com/dp/B00AQSH996/ref=cm_ sw_r_cp_api_5v5.yb1NY6136 Plug it into your mini's provided iPhone dock cable (below the center controls in that empty space in front of the gear shift). Your iPhone will connect via Bluetooth simultaneously to the MINI and your BT audio receiver and voila! This is the set up that I use & it works great. Sporadically I have issues with volume control (where I'll want my music volume down and it'll turn navigation down & I'll have to disconnect from both Bluetooth devices and reconnect to fix), but it's otherwise great, an inexpensive fix & sounds a lot less irritating than your current set up. I see your post was 2 years ago, but I still wanted to reply in case you haven't yet found a better solution, or, if you have, perhaps your solution is better than mine and you would be kind enough to share it with me! Cheers!

How to play music through Bluetooth in my mini Cooper 2013